Entropy solutions to noncoercive nonlinear elliptic equations with measure data

Abstract

Let Ω ⊆ ℝN be a bounded domain. In this article, we investigate the existence of entropy solutions to the nonlinear elliptic problem -div (|∇u|(p-2) ∇u + c(x)uγ / (1 + |u|)θ(p-1) + b(x)|∇u|λ / (1 + |u|θ(p-1) = μ, x ∈ Ω, u(x) = 0, x ∈ ∂Ω, where μ is a diffuse measure with bounded variation on Ω, 0 ≤ θ < 1 is a positive constants, 1 < p < N, 0 < γ ≤ p - 1, 0 < λ ≤ p - 1, c(x) and b(x) belong to appropriate Lorentz spaces.